Dissipative Dynamics of Enzymes

Amila Ariyaratne, Chenhao Wu, Chiao-Yu Tseng, and Giovanni Zocchi

Phys. Rev. Lett. 113, 198101 – Published 4 November 2014

Abstract

We explore enzyme conformational dynamics at sub-Å resolution, specifically, temperature effects. The ensemble-averaged mechanical response of the folded enzyme is viscoelastic in the whole temperature range between the warm and cold denaturation transitions. The dissipation parameter $γ$ of the viscoelastic description decreases by a factor of 2 as the temperature is raised from 10 to $45 ° C$ ; the elastic parameter $K$ shows a similar decrease. Thus, when probed dynamically, the enzyme softens for increasing temperature. Equilibrium mechanical experiments with the DNA spring (and a different enzyme) also show, qualitatively, a small softening for increasing temperature.

Received 8 April 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.198101

Authors & Affiliations

Amila Ariyaratne, Chenhao Wu, Chiao-Yu Tseng, and Giovanni Zocchi^*

Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA

^*zocchi@physics.ucla.edu

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Vol. 113, Iss. 19 — 7 November 2014

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Images

Figure 1
Experimental setup. The enzyme under study is covalently coupled to a Au-coated glass slide on one side and a 20 nm GNP on the opposite side. The negatively charged GNPs are driven by an oscillating electric field in a parallel plate capacitor arrangement in buffered saline solution. The amplitude of oscillation of the GNPs is measured by evanescent wave scattering with phase-locked detection. The scattered intensity represents the ensemble-averaged position of $\sim 1 0^{8}$ GNPs, which oscillates at the driving frequency.
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Figure 2
Amplitude of the enzyme’s deformation vs frequency of the drive force. The different curves correspond to different temperatures; the amplitude of the drive force is fixed. (a) Measurements at and above RT all obtained from the same sample; (b) measurements at and below RT, similarly obtained from one sample. Each experimental point represents the average of typically five frequency sweeps; error bars indicate standard deviations. All curves have similar features: a $1 / ω$ divergence for low frequencies (characteristic of viscous flow response) and a plateau for high frequencies (characteristic of elastic response). The corner frequency $ω_{c}$ , where the behavior changes from elastic to viscous, increases monotonically with increasing temperature, as does the deformation amplitude in the plateau region. In short, the enzyme softens with increasing temperature. The lines are two-parameter fits using the form of Eq. (2), which is derived from the Maxwell model of viscoelasticity.
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Figure 3
Temperature dependence of the viscoelastic parameters. The circles show the ratio of the dissipation parameter $γ$ at the given temperature and at $22 ° C$ . The squares show the same ratio for the elastic parameter $K$ . The values are determined from the parameters $A$ , $B$ obtained from the fits of Fig. 2, using $1 / A \propto γ$ and $B / A \propto K$ , according to Eqs. (1) and (2). Both $γ$ and $K$ decrease monotonically with increasing temperature. Inset: Arrhenius plot of the corner frequency $ω_{c}$ .
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Figure 4
Cartoon of the RLuc chimera. The enzyme is Renilla Luciferase (PDB 2PSJ), and the DNA spring is cut out from the structure L8sa in the MD simulation of Lankas et al. [29], which shows kinking in the stressed DNA. The DNA spring is attached at sites 161 and 188 (mutated to cysteins) on the surface of the enzyme.
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Figure 5
Ratio of the enzymatic activity with and without stress, for low stress (solid bars) and high stress (shaded bars), at different temperatures. Enzymatic activity (a measure of the speed of the reaction) is obtained as the luminescence intensity integrated over time. The ratios are obtained from aliquots of the same chimera sample in the ss form (no stress), ds form with a nick (low stress), ds form without nick (high stress), with each aliquot maintained at the same temperature. The ratio is always $< 1$ because mechanical stress decreases the activity of the enzyme. The ratio of activity with and without stress decreases with increasing temperature, qualitatively indicating that the enzyme becomes mechanically softer. The circles show the relative activity of the unstressed enzyme at the different temperatures, normalized to 1 at $25 ° C$ . The dotted line is a guide to the eye.
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